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A drunk man will find his way home, but a drunk bird may get lost forever
This elegant quote, which captures the essence of the mathematical fact that a 2-dimensional random walk is recurrent while in higher dimensions it is not, is attributed to Shizuo Kakutani. However, the original proof is due to George Pólya [1]. A -dimensional lattice is defined as a graph whose vertices are all points in with […]
A reflection on the latest developments in AI
ChatGPT, DeepSeek, and other large language models are revolutionizing the way we interact with information, automate tasks, and understand natural language. Furthermore, there is a lot of discussion around the dangers behind AI. I just came across a video in my feed featuring an interview with neural networks pioneer Geoff Hinton, who has received both […]
Rayleigh’s monotonicity principle and AM-GM-HM inequalities
Rayleigh’s monotonicity principle states that if the resistances of a circuit of resistors are increased, the effective resistance between any two points can only increase. If they are decreased, they can only decrease. You can find a short proof in the Doyle-Snell book right here. One can use this intuitive principle to prove classic and […]
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